Incommensurate Diffusion in Confined Systems

Molecular simulations corroborate the existence of the disputed window effect, i.e., an increase in diffusion rate by orders of magnitude when the alkane chain length increases so that the shape of the alkane is no longer commensurate with that of a zeolite cage. This window effect is shown to be characteristic for molecular sieves with pore openings that approach the diameter of the adsorbate. Furthermore, the physical compatibility between the adsorbate and the adsorbent has a direct effect on the heat of adsorption, the Henry coefficients, the activation energy, and the frequency factors.

Figure 1

The reaction coordinate $q$ is defined as the position of the second bead of a chain mapped orthogonal to the axis of projection (the line perpendicular to the window). The resulting free energy profile $F(q)$ indicates a high free energy barrier at the position of the window $q^{*}$ separating cages $A$ and $B$. On the right-hand side we show two pictures: the unit cell of ERI in 3D (top), and the connectivity of the cages within the unit cell (bottom). At infinite dilution the molecules perform a random walk on a lattice spanned by the cage centers.

Figure 2

Diffusion coefficients as a function of chain length at 600 K for ERI-, CHA-, and LTA-type zeolite; △ ERI-type silica simulation results, ▲ experimental results of Gorring [8], * Cavalcante et al. [13], ● Magalhães, Laurence, and Conner [14]; ▽ CHA-type silica simulation results, ▼ experimental results of Gorring et al. [26]; ◇ LTA-type silica simulation results, ◆ experiment compiled in Ref. 7.

Figure 3

Activation energies obtained from fitting diffusion simulation results at 300, 400, 500, 600, and 700 K to the Arrhenius law compared to the experimental results taken from Gorring [8], Cavalcante et al. [13], and Magalhães, Laurence, and Conner [14].

Figure 4

The free energy difference between maximum and minimum for ERI-type silica at 600 K.

Figure 5

Henry coefficients in OFF-, ERI-, CHA-, and LTA-type silica as a function of chain length at 600 K.